Quasicrystals (QC) are binary or ternary alloys showing rotational symmetries incompatible with classical crystallography. Since their discovery in 1984 it has been a long standing question how and to which extend the extraordinary physical properties of QC are related to their aperiodic atomic structure. This question is intimately related to the nature of the valence electronic states in this materials, where Bloch states do no longer exist due to the absence of translational symmetry. In this respect the concept of critical electron states and associated "spiky" density of states has emerged, which is still controversially discussed as no signs of a spiky density of states for QC could be experimentally observed e.g. by photoelectron emission spectroscopy measuring the total density of states.
We have used low temperature (5 K) scanning tunnelling microscopy (STM) and spectroscopy (STS) on the (10-100) surface of the d-AlNiCo QC to relate the local atomic structure to the local density of states (LDOS). The (10-100) surface has been chosen due to the fact that we will find periodic atomic arrangement along the (00001) direction and aperiodic atomic arrangement in the (01000) direction. We will discuss the aperiodic terrace sequence on this surface and compare the characteristic terrace step heights with the sequence of characteristic atomic clusters of the XRD derived model structure by Steurer, Deloudie et al. for the d-AlNiCo. Atomically resolved STM images show that the expected 0.4 nm periodicity of the surface is only visible in rather small stripe like regions which are arranged according to a Fibonacci sequence in the aperiodic (01000) direction, the regions in between show complex reconstruction with periodicities of integer multiples of 0.4 nm. Using STS mapping we will show that indications of a spiky LDOS can be found on this surface with electron states localised in energy, yet showing a periodic intensity modulation along the periodic direction of the surface. The results will be compared to STS investigations of the 5-fold and 2-fold surface of the i-AlPdMn QC. We conclude that critical states might well exist in QC, yet the associated spiky density of states is only visible in the LDOS on the nm scale.
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